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 A092634 a(n) = 1 - Sum_{k=2..n} k*k!. 1
 -3, -21, -117, -717, -5037, -40317, -362877, -3628797, -39916797, -479001597, -6227020797, -87178291197, -1307674367997, -20922789887997, -355687428095997, -6402373705727997, -121645100408831997, -2432902008176639997 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 REFERENCES Appeared in University of Texas Interscholastic League High School Number Sense District Test, 2004. LINKS G. C. Greubel, Table of n, a(n) for n = 2..445 Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA Conjecture: a(n) +(-n-3)*a(n-1) +(2*n+1)*a(n-2) +(-n+1)*a(n-3)=0. - R. J. Mathar, Sep 27 2014 a(n) = 3 - (n+1)!. - Michel Marcus, Jun 07 2020 From G. C. Greubel, Jun 07 2020: (Start) a(n) = 3 - !(n+2) + !(n+1) = 3 - A003422(n+2) + A003422(n+1). E.g.f.: 3*exp(x) - (3 - 3*x + x^3)/(1-x)^2. (End) MAPLE A092634:= n-> 3-(n+1)!: seq(A092634(n), n=2..20); # G. C. Greubel, Jun 07 2020 MATHEMATICA Table[i; 1 - Sum[n n!, {n, 2, i}], {i, 2, 20}] PROG (PARI) a(n) = 1 - sum(k=2, n, k*k!); \\ Michel Marcus, Jun 07 2020 (Sage) [3-factorial(n+1) for n in (2..20)] # G. C. Greubel, Jun 07 2020 CROSSREFS Cf. A033312. Sequence in context: A309670 A121140 A005057 * A178537 A084159 A046727 Adjacent sequences:  A092631 A092632 A092633 * A092635 A092636 A092637 KEYWORD sign AUTHOR Doug Ray (draymath(AT)iastate.edu), Apr 11 2004 STATUS approved

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)